试验验证和数值仿真是评估结构强度的两种典型方法，然而基于离散传感器的试验验证方法难以保证结构应力监测覆盖度，数值仿真方法又因为对物理实体的简化和理想化处理而导致应力结果精度不足，如何综合利用两种强度评估方法的优势并进行数据融合以实现结构应力场监测是一个具有挑战性的问题。本研究提出了一种面向结构静力试验监测的数字孪生（Digital Twin for Structural Static Test Monitoring, DT-SSTM）方法，可获得高精度的结构静力试验数字孪生模型，以实现结构应力场的实时监测与强度评估。DT-SSTM方法包括离线、在线两个阶段。离线阶段，采用梯度提升树（Gradient Boosting Decision Tree, GBDT）算法对仿真数据进行训练，建立预训练模型。在线阶段，基于集成学习理论，采用Stacking算法对试验数据响应值与预训练模型响应值之间的残差进行训练并建立残差模型。通过叠加预训练模型与残差模型实现多源数据融合，建立高精度的数字孪生模型。最后，开展了开口矩形壁板轴向拉伸试验来验证DT-SSTM方法的有效性。结果表明，DT-SSTM方法能够建立高精度的结构静力试验数字孪生模型，且相比同类数据融合方法具有更高的全局、局部预测精度以及融合效率，为结构应力场实时监测提供了一种新颖的解决方案。
Experimental validation and numerical simulation are two typical methods for evaluating the structural strength, however, the experimental validation method based on sparse sensors is difficult to ensure the coverage of the structural stress monitoring, and the numerical simulation method may lead to the insufficient accuracy of stress results due to the simplification and idealization of physical entities. Therefore, it is a challenging issue to comprehensively utilize the advantages of these two methods of strength evaluation and carry out data fusion to achieve the full-field structural stress monitoring. In this study, the digital twin for structural static test monitoring (DT-SSTM) method is proposed, which can obtain a high-precision digital twin model of structural static test to realize the real-time monitoring of the structural stress fields and the structural strength evaluation. The DT-SSTM method includes two stages: offline and online stages. In the offline stage, the Gradient Boosting Decision Tree (GBDT) algorithm is used to train the simulation data and build a pre-trained model. In the online stage, based on the ensemble learning concept, the Stacking algorithm is used to train the residuals between the response values of the experimental data and the response values of the pre-training model, and then the residual model is established. Multi-source data fusion is carried out by combining the pre-trained model with the residual model to establish a high-precision digital twin model. Finally, the open-hole rectangular plate under axial tension is tested to validate the effectiveness of the DT-SSTM method. Results show that the DT-SSTM method can establish a high-precision digital twin model of the structural static test with higher global prediction accuracy, local prediction accuracy and data fusion efficiency compared with the similar data fusion methods, providing a novel solution for the real-time monitoring of structural stress fields.
[1] JIN S S, KIM S T, PARK Y H. Combining point and distributed strain sensor for complementary data-fusion: A multi-fidelity approach[J]. Mechanical Systems and Signal Processing, 2021, 157: 107725.
[2] KIM S, CHOI J-H, KIM NH. Data-driven prognostics with low-fidelity physical information for digital twin: physics-informed neural network[J]. Structural and Multidisciplinary Optimization, 2022, 65(9): 1-16.
[3] LI L, LEI B, MAO C. Digital twin in smart manufac-turing[J]. Journal of Industrial Information Integration. 2022, 26, 100289.
[4] LI C, MAHADEVAN S, LING Y, et al. Dynamic bayesian network for aircraft wing health monitoring digital twin[J]. AIAA Journal, 2017, 55(3): 930-941.
[5] LIM KYH, ZHENG P, CHEN C-H, et al. A digital twin-enhanced system for engineering product family design and optimization[J]. Journal of Manufacturing Systems, 2020, 57: 82-93.
[6] TAO F, ZHANG H, LIU A, et al. Digital twin in indus-try: state-of-the-art[J]. IEEE Transactions on Industrial Informatics, 2019, 15(4): 2405-2415.
[7] WANG S, LAI X, HE X, et al. Building a trustworthy product-level shape-performance integrated digital twin with multifidelity surrogate model[J]. Journal of Me-chanical Design, 2022, 144(3): 031703.
[8] XIA M, SHAO H, WILLIAMS D, et al. Intelligent fault diagnosis of machinery using digital twin-assisted deep transfer learning[J]. Reliability Engineering & System Safety, 2021, 215: 107938.
[9] GHOSH M, WU L, HAO Q, et al. A random forest with multi-fidelity Gaussian process leaves for model-ing multi-fidelity data with heterogeneity[J]. Comput-ers & Industrial Engineering, 2022, 174: 108746.
[10] 李增聪, 田阔, 赵海心. 面向多级加筋壳的高效变保真度代理模型[J]. 航空学报, 2020, 41(7): 623435-623435.
LI Z C, TIAN K, ZHAO H X. Efficient variable-fidelity models for hierarchical stiffened shells[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(7): 623435-623435 (in Chinese).
[11] TIAN K, LI ZC, HUANG L, et al. Enhanced variable-fidelity surrogate-based optimization framework by Gaussian process regression and fuzzy clustering[J]. Computer Methods in Applied Mechanics and Engi-neering, 2020, 366: 113045.
[12] LI ZC, ZHANG S, LI H, et al. On-line transfer learn-ing for multi-fidelity data fusion with ensemble of deep neural networks[J]. Advanced Engineering Informatics, 2022, 53: 101689.
[13] CHEN J, MENG C, GAO Y, et al. Multi-fidelity neural optimization machine for Digital Twins[J]. Structural and Multidisciplinary Optimization, 2022, 65(12): 1-15.
[14] LI K, WANG S, LIU Y, et al. An integrated surrogate modeling method for fusing noisy and noise-free da-ta[J]. Journal of Mechanical Design, 2022, 146(6): 061701.
[15] LAI X, HE X, PANG Y, et al. A scalable digital twin framework based on a novel adaptive ensemble surro-gate model[J]. Journal of Mechanical Design, 2023, 145(2): 021701.
[16] NATEKIN A, KNOLL A. Gradient boosting machines, a tutorial[J]. Frontiers in neurorobotics, 2013, 7: 21.
[17] TING K M, WITTEN I H. Stacking bagged and dagged models[J], 1997.
[18] GANAIE M A, HU M, MALIK A K, et al. Ensemble deep learning: A review[J]. Engineering Applications of Artificial Intelligence, 2022, 115: 105151.
[19] GUNN S R. Support vector machines for classification and regression[J]. ISIS technical report, 1998, 14(1): 5-16.
[20] TIAN K, LI ZC, ZHANG JX, et al. Transfer learning based variable-fidelity surrogate model for shell buck-ling prediction[J]. Composite Structures, 2021, 273: 114285.
[21] GISELLE FERNáNDEZ-GODINO M, PARK C, KIM NH, et al. Review of multi-?delity models[J]. arXiv preprint arXiv:160907196, 2016.
[22] ZHOU Q, SHAO XY, JIANG P, et al. An active learn-ing metamodeling approach by sequentially exploiting difference information from variable-fidelity models[J]. Advanced Engineering Informatics, 2016, 30(3): 283-297.
[23] TIAN K, WANG B, ZHANG K, et al. Tailoring the optimal load-carrying efficiency of hierarchical stiff-ened shells by competitive sampling[J]. Thin-Walled Structures, 2018, 133: 216-225.
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